(orthonormal basis) there exists a functionΦ∈V0, called a scaling function, such that the system {Φ(t-m)}m∈ℤ} is an orthonormal basis in V0.

Notes

Multiresolution analysis, particularly scaling functions, are used to derive wavelets. The Vj are called approximation spaces. Several choices of scaling functions may exist for a given set of approximation spaces— each determines a unique multiresolution analysis.